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## Re: [Help-glpk] binary boolean

**From**: |
Michael Hennebry |

**Subject**: |
Re: [Help-glpk] binary boolean |

**Date**: |
Sun, 6 May 2012 00:33:10 -0500 (CDT) |

**User-agent**: |
Alpine 1.00 (DEB 882 2007-12-20) |

On Sat, 5 May 2012, Andrew Makhorin wrote:

3. Yet another description (as pointed out by Erwin and Michael)
z >= x
z >= y
z <= x+y
It is a good description, because all inequalities are facet-defined
(until the mip instance includes other constraints).

Together with z<=1, it is *the* sensible description.
There are no other facets.
In general, { (x, y, f(x,y)) : (x, y) in {0, 1}**2 }
has precisely four facets.
Since their bounds are not facets, but are implied by facets,
it might be useful to require that x and y never be non-basic.
Likewise, z should not be non-basis at zero.
The situation is more complicated for larger numbers of variables.
--
Michael address@hidden
"On Monday, I'm gonna have to tell my kindergarten class,
whom I teach not to run with scissors,
that my fiance ran me through with a broadsword." -- Lily

**[Help-glpk] binary boolean**, *Zvonko Bregar*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Erwin Kalvelagen*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/03`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/04`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/04`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**,
*Michael Hennebry* **<=**
**Re: [Help-glpk] binary boolean**, *Andrew Makhorin*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Yaron Kretchmer*, `2012/05/05`
**Re: [Help-glpk] binary boolean**, *Michael Hennebry*, `2012/05/04`